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For the mathematical thing, for a chain of random events to occur involving the formation of life, it is critical that all connections are positive or else the process begins again. This is outside of trial and error because there is nobody to test the results and modify and inputs. Assuming a 50/50 chance, even a chain involving 10 parts would have a 1/1024 chance of coming together. I'll be honest and say I don't know the odds involved in forming the simplest amino acids, and I probably should check that out. >snip<